The concept of average degree-eccentricity matrix ADE(G) of a connected graph $G$ is introduced. Some coefficients of the characteristic polynomial of ADE(G) are obtained, as well as a bound for the eigenvalues of ADE(G). We also introduce the average degree-eccentricity graph energy and establish bounds for it.

The energy E(G) of a graph G is the sum of the absolute values of the eigenvalues of G. In this article we consider the problem whether generalized Fibonacci constants $varphi_n$ $(ngeq 2)$ can be the energy of graphs. We show that $varphi_n$ cannot be the energy of graphs. Also we prove that all natural powers of $varphi_{2n}$ cannot be the energy of a matroid.

This paper formulates pixel labelling as a series of two-category classification. Unlike existing techniques, which assign a determinate label to each pixel, we assign a label set to each pixel and shrink the label set step by step. Determinate labelling is achieved within log2n (n is size of label set) steps. In each step, we bisect the label set into two subsets and discard the one with highe...

Knowledge representation of networked systems is fundamental in many disciplines. To date, existing methods for learning primarily focus on networks with simplex labels, yet real-world objects (nodes) are inherently complex nature and often contain rich semantics or labels. For example, a user may belong to diverse interest groups social network, resulting multi-label applications. A network no...

Recently, a family of global, non-submodular energy functions has been proposed that is expressed as coupling edges in a graph cut. This formulation provides a rich modelling framework and also leads to efficient approximate inference algorithms. So far, the results addressed binary random variables. Here, we extend these results to the multi-label case, and combine edge coupling with move-maki...